Moderate -0.8 This is a straightforward application of the binomial theorem requiring students to identify the correct term (r=4) and calculate using the formula. It's simpler than average as it involves direct substitution into a standard formula with no algebraic manipulation or problem-solving required, though the arithmetic with larger numbers prevents it from being trivial.
Annotate if partially correct; allow 4 for \(70\,000x^4\) www
M3 for \(35 \times 5^3 \times 2^4\) oe
M3
May be unsimplified; do not allow 35 in factorial form unless evaluated later
or M2 for two of these elements multiplied
M2
Or for all three elements seen together (e.g. in table) but not multiplied
or M1 for 35 oe, or for 1 7 21 35 35 21 7 1 row of Pascal's triangle seen
M1
Throughout, condone \(x\)s included e.g. \((2x)^4\); may also include other terms in expansion; mark coefficient of \(x^4\)
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| 70 000 | 4 marks total (www) | Annotate if partially correct; allow 4 for $70\,000x^4$ www |
| M3 for $35 \times 5^3 \times 2^4$ oe | M3 | May be unsimplified; do not allow 35 in factorial form unless evaluated later |
| or M2 for two of these elements multiplied | M2 | Or for all three elements seen together (e.g. in table) but not multiplied |
| or M1 for 35 oe, or for 1 7 21 35 35 21 7 1 row of Pascal's triangle seen | M1 | Throughout, condone $x$s included e.g. $(2x)^4$; may also include other terms in expansion; mark coefficient of $x^4$ |
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